Advertisements
Advertisements
प्रश्न
The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.
Advertisements
उत्तर
Let a, b be the two numbers.
.'. a + b = 7 and a3 + b3 = 133
(a + b)3 = a3 + b3 + 3ab (a + b)
⇒ (7)3 = 133 + 3ab (7)
⇒ 343 = 133 + 21ab
⇒ 21ab = 343 - 133 = 210
⇒ 21ab = 210
⇒ ab= 10
Now a2 + b2 = (a + b)2 - 2ab
= 72 - 2 x 10 = 49 - 20 = 29
APPEARS IN
संबंधित प्रश्न
Expand : ( x + 8 ) ( x + 10 )
Expand : `( 3a + 2/b )( 2a - 3/b )`
If a2 + b2 + c2 = 35 and ab + bc + ca = 23; find a + b + c.
If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.
If x+ y - z = 4 and x2 + y2 + z2 = 30, then find the value of xy - yz - zx.
If a + `1/a` = m and a ≠ 0 ; find in terms of 'm'; the value of :
`a - 1/a`
If a2 + b2 = 34 and ab = 12; find : 3(a + b)2 + 5(a - b)2
If a2 + b2 = 34 and ab = 12; find : 7(a - b)2 - 2(a + b)2
The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares
If 3a + 5b + 4c = 0, show that : 27a3 + 125b3 + 64c3 = 180 abc
